Loan Payment Calculator
Estimate monthly payment, total paid, and total interest for an amortizing loan at a fixed rate.
Formula and help
Auto Loan Calculator Formula and Help
Learn how this calculator works, what formula it uses, and which assumptions sit behind the estimate.
Back to calculatorHow it works
The Auto Loan Calculator estimates a level monthly payment for a fixed-rate vehicle loan. It subtracts the entered down payment and trade-in value from the vehicle price, floors the financed amount at zero, and then amortizes that amount over the selected term. The result shows financed amount, monthly payment, total loan payments, and total interest before sales tax, title and registration fees, dealer add-ons, rebates, negative equity, insurance, maintenance, or lender underwriting.
Use this calculator when you want a mechanical estimate from vehicle price, down payment, trade-in value, entered annual rate, and term months. Use Loan Payment for a generic fixed-rate loan, APR when fees need an APR-style cash-flow estimate, Payment or Amortization for broader payment and schedule questions, Cash Back or Low Interest for two vehicle-incentive offers, Lease for lease assumptions, and Debt-to-Income or Budget for monthly pressure. Use CFPB auto-loan materials, Regulation Z, FTC dealer-advertising and financing guidance, lender disclosures, state DMV or tax authorities, and legal sources for real APR, Truth in Lending disclosures, taxes, registration, rebates, add-ons, eligibility, approval, or jurisdiction-specific claims.
Formula notes
This formula page covers the app's Auto Loan Calculator: a fixed-rate vehicle-loan estimate from vehicle price, down payment, trade-in value, annual rate, and term in months. It estimates financed amount, monthly payment, total paid, and total interest before sales tax, title, registration, dealer fees, rebates, insurance, maintenance, negative equity, lender underwriting, or legal lending disclosures.
P = max(0, Price - Down - Trade); R = annualRate / 100; m = R / 12; PMT = P * m / (1 - (1 + m)^-n); zero rate: PMT = P / n; Total = PMT * n; Interest = Total - P
The calculator subtracts down payment and trade-in value from the vehicle price, floors the financed amount at zero, converts the entered annual rate into a monthly rate, solves the fixed monthly payment, then estimates total paid and total interest across the selected month count.| Symbol | Meaning | How this page uses it |
|---|---|---|
| Price | Vehicle price | The Vehicle price input before the calculator subtracts the down payment or trade-in value. It is not an out-the-door purchase price with tax, title, registration, dealer fees, or add-ons. |
| Down | Down payment | The cash amount entered as Down payment and subtracted from the vehicle price before the loan payment is estimated. |
| Trade | Trade-in value | The Trade-in value input subtracted from the vehicle price. The app treats it as a simple positive offset, not as a payoff, negative-equity, tax-credit, or dealer-appraisal model. |
| P | Financed amount | The app's payment base: vehicle price minus down payment minus trade-in value, floored at zero for calculation safety. |
| R | Annual rate as a decimal | The Annual rate field divided by 100. A 7 percent entry becomes 0.07. This input is not automatically a legal APR disclosure. |
| m | Monthly rate | The decimal annual rate divided by 12. The app assumes monthly payment periods and does not expose a separate compounding-frequency field. |
| n | Term in months | The Term in months input. The calculator uses it directly as the count of level monthly payments. |
| PMT | Monthly payment | The level monthly payment before taxes, fees, insurance, rebates, add-ons, payoff balances, lender charges, or contract-specific terms. |
| Total | Total paid | Monthly payment multiplied by term months before display rounding. |
| Interest | Total interest | Total paid minus the financed amount. |
Step by step
- Read vehicle price, down payment, trade-in value, annual rate, and term in months from the calculator inputs.
- Subtract down payment and trade-in value from vehicle price.
- Apply the app's safety floor with P = max(0, Price - Down - Trade), so over-offset inputs do not create a negative loan balance.
- Convert the entered annual percentage rate into a decimal annual rate by dividing by 100.
- Convert the decimal annual rate into the app's monthly rate assumption by dividing by 12.
- If the monthly rate is 0, divide the financed amount by the term in months to get the level monthly payment.
- Otherwise, solve the fixed amortizing payment with P times m divided by 1 minus (1 + m) raised to negative n.
- Calculate total paid as monthly payment times term months.
- Calculate total interest as total paid minus the financed amount.
- Round displayed currency outputs to two decimals after the full-precision calculation.
- Treat APR, finance charge, amount financed, total-of-payments disclosure, Truth in Lending, taxes, title, registration, rebates, negative equity, add-ons, lender underwriting, dealer claims, and local legal rules as separate topics that need CFPB, Regulation Z, FTC, lender, dealer, state DMV, tax-authority, regulator, or legal source checks.
Sources and validation
This calculator is an original implementation based on documented formulas, app-specific assumptions, deterministic fixtures, edge cases, rounding policy tests, and internal validation. It is not copied from a single source.
Outputs are checked with deterministic fixtures, edge cases, rounding policy tests, and internal independent comparator checks where overlapping outputs are available. The result remains an educational estimate, not a quote, approval, tax answer, or personalised advice.
- CFPB auto-loan key terms and offer-comparison guidance should be used before copy defines APR, interest rate, loan term, down payment, trade-in, negative equity, amortization, total cost, or payment-shopping context.
- CFPB Truth-in-Lending auto-loan disclosure materials and Regulation Z sections 1026.18 and 1026.22 should be used before copy discusses legal APR, finance charge, amount financed, payment schedule, total of payments, disclosure accuracy, or creditor disclosure requirements.
- FTC financing-or-leasing guidance, lender or dealer documents, state DMV and tax authorities, state regulators, and legal sources should be used before copy makes product-specific, approval, tax, title, registration, rebate, add-on, advertising, negative-equity, or jurisdiction-specific claims.
See the Calcs.finance methodology for the full review approach.
Assumptions
- The calculation models one fixed-rate vehicle loan with equal monthly payments. The entered term in months is the payment count, and the entered annual rate is converted to a simplified monthly rate.
- Vehicle price, down payment, and trade-in value are simple offsets. The trade-in field is not a payoff amount, negative-equity amount, tax-credit rule, dealer appraisal, or guarantee that the trade-in value will be available. If down payment plus trade-in exceed vehicle price, the financed amount is floored at zero.
- The calculator excludes sales tax, title, registration, documentation fees, dealer add-ons, optional credit insurance, GAP, rebates, maintenance, insurance, variable rates, prepayment rules, late fees, credit approval, and legal disclosures. Scoped independent comparator checks pass for overlapping fixed-payment and zero-rate outputs, while CFPB, Regulation Z, FTC, lender, state DMV, state tax, and legal sources are needed before making real APR, Truth in Lending, advertising, registration, tax, product-specific, eligibility, approval, or jurisdiction-specific claims. Results are educational estimates, not financial, legal, tax, lending, credit, consumer-rights, regulatory, or personalised advice.
Common mistakes to avoid
- Reading the monthly payment as the full ownership cost. The calculator does not include taxes, title and registration fees, dealer add-ons, insurance, fuel, maintenance, repairs, parking, or depreciation.
- Treating the entered annual rate as the legal APR or a dealer quote. APR disclosures can include required fees and legal timing rules that this calculator does not model.
- Entering a trade-in payoff or negative-equity amount as if it were positive trade-in value, or reading Total paid as the total purchase cost. Total paid is only the modeled loan-payment stream after the simplified financed amount is calculated.
Worked example
Default example: $35,000 vehicle, $5,000 down, $3,000 trade, 7 percent, 60 months
The default calculator inputs use a $35,000 vehicle price, a $5,000 down payment, a $3,000 trade-in value, a 7 percent annual rate, and a 60-month term.
- Subtract the $5,000 down payment and $3,000 trade-in value from the $35,000 vehicle price.
- The financed amount is $27,000 because $35,000 - $5,000 - $3,000 = $27,000.
- Convert 7 percent to the decimal annual rate 0.07.
- Divide 0.07 by 12 to get a monthly rate of about 0.0058333.
- Use n = 60 monthly payments.
- Apply PMT = P * m / (1 - (1 + m)^-n) with P = $27,000, m about 0.0058333, and n = 60.
- The calculator reports a monthly payment of $534.63.
- Total paid is the full-precision monthly payment times 60, reported as $32,077.94.
- Total interest is total paid minus the $27,000 financed amount, reported as $5,077.94.
- The zero-rate fixture uses a $22,000 vehicle, $3,000 down, $1,000 trade-in value, 0 percent, and 36 months. It finances $18,000, divides by 36, and reports a $500 monthly payment, $18,000 total paid, and $0 interest.
The formula can help compare how purchase price, down payment, trade-in value, rate, and term change the mechanical loan estimate. It does not show a lender quote, dealer out-the-door price, approval, legal disclosure, or personalised vehicle-financing recommendation.
What this formula does not include
- The calculator models one fixed-rate vehicle loan with level monthly payments. It does not model variable rates, promotional-rate changes, interest-only periods, balloon payments, deferred payments, late fees, prepayment penalties, or payment holidays.
- The annual rate input is divided by 12 for the payment formula and is not automatically a legal APR. APR, finance charge, amount financed, payment schedule, total of payments, and Truth in Lending copy need CFPB, Regulation Z, lender, or legal source checks.
- The financed amount floor at zero prevents negative payment bases when down payment plus trade-in value exceed vehicle price, but it does not model cash due back, equity refunds, dealer appraisal adjustments, trade payoff amounts, or negative equity.
- No sales tax, title, registration, documentation fee, dealer fee, origination charge, lien fee, destination charge, warranty, gap coverage, credit insurance, maintenance plan, rebate, manufacturer incentive, lender credit, or add-on product is included.
- No credit score, underwriting, approval odds, loan-to-value test, collateral valuation, income verification, debt-to-income review, lender contract, dealer contract, advertising rule, or jurisdiction-specific lending rule is modeled.
- The trade-in input is a simple positive offset. It does not decide whether a dealer will accept the trade, how payoff balance is handled, whether negative equity is rolled in, or whether the trade changes sales-tax treatment.
- The page is not an amortization schedule, payoff quote, lease comparison, cash-back-versus-low-interest analysis, title or tax lookup, insurance estimate, vehicle affordability test, or regulated consumer-credit disclosure.
- Package fixtures currently cover the default fixed-rate branch and the 0 percent zero-rate branch; use the independent comparator only as an overlapping-payment comparator because it can include sales tax, fees, trade-in state, negative-equity, and payoff fields this app omits.
- Use CFPB auto-loan terms and offer-comparison guidance, CFPB Truth-in-Lending disclosure materials, Regulation Z, FTC dealer-financing guidance, lender or dealer documents, state DMV and tax authorities, state regulators, or legal sources before making real APR, total-cost, tax, title, registration, rebate, add-on, approval, advertising, negative-equity, or jurisdiction-specific claims.
- The result is an educational estimate from the entered assumptions, not financial, tax, legal, lending, credit, consumer-rights, regulatory, vehicle-purchase, or personalised advice.
Terms used in this calculator
- Amount financed
- The vehicle price left after subtracting the entered down payment and trade-in value. This calculator floors the amount at zero and then amortizes it over the selected months.
- Monthly payment
- The equal payment estimated for each month of the selected term. It uses the fixed-rate payment formula unless the entered annual rate is zero.
- Entered annual rate
- The percentage rate entered by the user for the simplified estimate. The calculator divides it by 100 and 12. It is not a legal APR disclosure or lender quote.
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Related next steps
- Auto loan calculatorReturn to the calculator and test vehicle price, down payment, trade, rate, and term assumptions.
- Loan payment calculatorUse this for the generic fixed-rate loan payment model without vehicle-specific inputs.
- Loan payment formula notesCompare the vehicle-loan estimate with the simpler amortized loan formula.
- APR calculatorUse this when selected finance charges and APR-style cash flows need a separate estimate.
- APR formula notesReview APR and lending-disclosure source boundaries before comparing offers.
- Payment calculatorUse this for broader fixed-term or fixed-payment payoff relationships.
- Payment formula notesReview fixed-term and fixed-payment solve modes.
- Interest rate calculatorUse this when amount, payment, and term imply an annual rate.
- Amortization calculatorUse this when month-by-month principal, interest, and balance matter.
- Debt-to-income calculatorEstimate monthly debt pressure separately from the vehicle-payment formula.
- Cash back or low interest calculatorCompare rebate and low-rate assumptions with a dedicated scenario calculator.
- Lease calculatorUse this when the vehicle question is a lease rather than a purchase loan.
- Loan calculator categoryBrowse adjacent loan, APR, payment, amortization, and payoff calculators.
- Loan calculator categorySee the full loan calculator category.
- Why results are estimatesReview why calculator outputs can differ from real quotes and contracts.
- MethodologySee how formula implementations are reviewed and validated.
- Editorial policyReview how finance content is written, checked, and corrected.
- DisclaimerReview the limits of educational calculator estimates.